For a n invertible matrix with a n LU factorization A = LU, both L and U

Question:

For a n invertible matrix with a n LU factorization A = LU, both L and U will be invertible and A-l = U-1 L-1. In Exercises, find L-1, U-1, and A-1 for the given matrix.
a. A in Exercise 1

b. A in Exercise 4

For a n invertible matrix with a n LU factorization

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-1285463247

4th edition

Authors: David Poole

See More Books

Question Posted: Apr 15, 2016 06:05 AM

See More Questions

Let A be an m n matrix with linearly independent columns. Explain why ATA must be an invertible matrix. Must AAT also be invertible? Explain.
1. If there exists an n n matrix A1 such that AA1 = In = A1A, then A1 is the ________ of A. 2. A matrix that has an inverse is invertible or ________. A matrix that does not have an inverse is...
1. Determinant of an Inverse Prove for invertible matrix A that 2. Do Determinants Commute? Let A and B be any two n ( n matrices. Explain why | AB | = | BA |. 1
In Exercises 1126, determine whether each equation defines y as a function of x. 4x = y 2
Consider the following financial data from the past year for Midwest Outdoor Equipment Corporation. Gross Income..........$25,240,000 Total Sales........... 24,324,000 Total Credit Sales............
Discuss the contemporary issues related to accounting for extractive activities.
The probability that a person will be able to swim 20 miles is 40%. Classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your...
1. How does Toyotas approach to social responsibility relate to the three concepts of social responsibility described in the text (profit responsibility, stakeholder responsibility, and societal...
Find y'' for y = 2+ y" = 53 X
Sentry, Inc. was started on January 1, Year 1. Year 1 Transactions 1. Acquired $20,000 cash by issuing common stock. 2. Earned $62,000 of revenue on account. 3. On October 1, Year 1, borrowed $12,000...
Generalize the definition of LU factorization to non square matrices by simply requiring U to be a matrix in row echelon form. With this modification, find an LU factorization of the matrices in...
The inverse of a matrix can also be computed by solving several systems of equations using the method of Example 3.34. For an n X n matrix A, to find its inverse we need to solve AX = In for the n...
If possible, solve the nonlinear system of equations. x - y = 3 x +y = 3
Indicate whether each of the following statements is true or false by writing T or F in the answer c olumn. It is legally permissible to delegate contract obligations to perform certain tasks.
Briefly describe how primary WWT differs from secondary WWT.
Indicate whether each of the following statements is true or false by writing T or F in t he a nswer c olumn. The parol evidence rule affects the enforceability of contracts that include oral or...
Indicate whether each of the following statements is true or false by writing T or F in the answer c olumn. A consumer can terminate a contract made in the home with a door-to-door salesperson within...
Rework part (d) of Problem 3-4 using the Fisher LSD method. What conclusions can you draw? Explain carefully how you modified the technique to account for unequal sample sizes. Problem 3-4 An...
The number (in billions) of pieces of mail handled by the U.S. Post Office each year from 2010 through 2019 can be approximated by P(t) = -0.003584t 4 - 0.01051t 3 + 0.7432t 2 - 6.508t + 171.7 where...
Suppose you won a financial literacy competition and are given FJS10000 to invest, with the condition that investment can be done either in, i) Invest in Unit trust of Fiji or Invest in Fijian...
Consider the dynamical system x k + 1 = Ax k . (a) Compute and plot x 0 ,x 1 ,x 2 ,x 3 , for x 0 (b) Compute and plot x 0 ,x 1 ,x 2 ,x 3 , for x 0 (c) Using eigenvalues and eigenvectors, classify the...
the given matrix is of the form In each case, A can be factored as the product of a scaling matrix and a rotation matrix. Find the scaling factor r and the angle of rotation. Sketch the first four...
the given matrix is of the form In each case, A can be factored as the product of a scaling matrix and a rotation matrix. Find the scaling factor r and the angle of rotation. Sketch the first four...
given l o g x 5 = l o g 5 x solve for x
Solve the formula 8 x 3 y = - 1 9 for y .
Q6 Find the total amount for of the current balance for each underwriter and find out top 10 richest underwriter Q7 Create a pivot table for the entire data and find out the total current balance for...

For a n invertible matrix with a n LU factorization A = LU, both L and U

Question:

1 1 0 1 5 2 001 010205 1 3-2-2 L 042042 -4-12-450 231200

Step by Step Answer:

a In Exercise 1 we have Then So that A 1 LU 1 U 1 L 1 ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Linear Algebra questions